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The way solutions are represented, or encoded, is usually the result of domain knowledge and experience. In this work, we combine MAP-Elites with Variational Autoencoders to learn a Data-Driven Encoding (DDE) that captures the essence of the highest-performing solutions while still able to encode a wide array of solutions. Our approach learns this data-driven encoding during optimization by balancing between exploiting the DDE to generalize the knowledge contained in the current archive of elites and exploring new representations that are not yet captured by the DDE. Learning representation during optimization allows the algorithm to solve high-dimensional problems, and provides a low-dimensional representation which can be then be re-used. We evaluate the DDE approach by evolving solutions for inverse kinematics of a planar arm (200 joint angles) and for gaits of a 6-legged robot in action space (a sequence of 60 positions for each of the 12 joints). We show that the DDE approach not only accelerates and improves optimization, but produces a powerful encoding that captures a bias for high performance while expressing a variety of solutions.

A new method for design space exploration and optimization, Surrogate-Assisted Illumination (SAIL), is presented. Inspired by robotics techniques designed to produce diverse repertoires of behaviors for use in damage recovery, SAIL produces diverse designs that vary according to features specified by the designer. By producing high-performing designs with varied combinations of user-defined features a map of the design space is created. This map illuminates the relationship between the chosen features and performance, and can aid designers in identifying promising design concepts. SAIL is designed for use with compu-tationally expensive design problems, such as fluid or structural dynamics, and integrates approximative models and intelligent sampling of the objective function to minimize the number of function evaluations required. On a 2D airfoil optimization problem SAIL is shown to produce hundreds of diverse designs which perform competitively with those found by state-of-the-art black box optimization. Its capabilities are further illustrated in a more expensive 3D aerodynamic optimization task.

Surrogate-assistance approaches have long been used in computationally expensive domains to improve the data-efficiency of optimization algorithms. Neuroevolution, however, has so far resisted the application of these techniques because it requires the surrogate model to make fitness predictions based on variable topologies, instead of a vector of parameters. Our main insight is that we can sidestep this problem by using kernel-based surrogate models, which require only the definition of a distance measure between individuals. Our second insight is that the well-established Neuroevolution of Augmenting Topologies (NEAT) algorithm provides a computationally efficient distance measure between dissimilar networks in the form of "compatibility distance", initially designed to maintain topological diversity. Combining these two ideas, we introduce a surrogate-assisted neuroevolution algorithm that combines NEAT and a surrogate model built using a compatibility distance kernel. We demonstrate the data-efficiency of this new algorithm on the low dimensional cart-pole swing-up problem, as well as the higher dimensional half-cheetah running task. In both tasks the surrogate-assisted variant achieves the same or better results with several times fewer function evaluations as the original NEAT.

The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique to 'illuminate' the problem space through the lens of chosen features has the potential to be a powerful tool for exploring design spaces, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination (SAIL) algorithm, introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites.
The ability of SAIL to efficiently produce both accurate models and diverse high-performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMA-ES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.

Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization algorithms because they produce diverse, high-quality solutions in a single run, instead of only a single near-optimal solution. Unfortunately, these algorithms currently require a large number of function evaluations, limiting their applicability. In this article we introduce a new illumination algorithm, Surrogate-Assisted Illumination (SAIL), that leverages surrogate modeling techniques to create a map of the design space according to user-defined features while minimizing the number of fitness evaluations. On a two-dimensional airfoil optimization problem SAIL produces hundreds of diverse but high-performing designs with several orders of magnitude fewer evaluations than MAP-Elites or CMA-ES. We demonstrate that SAIL is also capable of producing maps of high-performing designs in realistic three-dimensional aerodynamic tasks with an accurate flow simulation. Data-efficient design exploration with SAIL can help designers understand what is possible, beyond what is optimal, by considering more than pure objective-based optimization.

The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique has the potential to be a powerful tool for design space exploration, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination algorithm (SAIL), introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites.
The ability of SAIL to efficiently produce both accurate models and diverse high performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMA-ES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.

Are quality diversity algorithms better at generating stepping stones than objective-based search?
(2019)

The route to the solution of complex design problems often lies through intermediate "stepping stones" which bear little resemblance to the final solution. By greedily following the path of greatest fitness improvement, objective-based search overlooks and discards stepping stones which might be critical to solving the problem. Here, we hypothesize that Quality Diversity (QD) algorithms are a better way to generate stepping stones than objective-based search: by maintaining a large set of solutions which are of high-quality, but phenotypically different, these algorithms collect promising stepping stones while protecting them in their own "ecological niche". To demonstrate the capabilities of QD we revisit the challenge of recreating images produced by user-driven evolution, a classic challenge which spurred work in novelty search and illustrated the limits of objective-based search. We show that QD far outperforms objective-based search in matching user-evolved images. Further, our results suggest some intriguing possibilities for leveraging the diversity of solutions created by QD.

The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Varia-tional Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions-but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinemat-ics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.